A Parametric Successive Underestimation Method for Convex Programming Problems with an Additional Convex Multiplicative Constraint
نویسندگان
چکیده
A bstract This paper addresses itself to an algorithm for a convex minimization problem with an additional convex multiplicative constraint. A convex multiplicative constraint is such that a product of two convex functions is less than or equal to some constant. It is shown that this non convex problem can be solved by solving a sequence of convex programming problems. The basic idea of this algorithm is to embed the original problem into a problem in a higher dimensional space and to apply a parametric programming technique. A branch-and-bound algorithm is proposed for obtaining an {-optimal solution in finitely many iterations. Computational results indicate that this algorithm is efficient for linear programs with an additional linear multiplicative constraint.
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